MATH 181 Study Guide - Final Guide: Scilab
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Problem 1 solution: compute the de nite integral: Solution: using the fundamental theorem of calculus part i, the value of the integral is: + 3# dx = ln |x| + 3x%5. = [17 ln |5| + 3(5)] [17 ln |1| + 3(1)] = 17 ln 5 + 15 0 3. Problem 2 solution: consider the function f (x) = 2x x2 on the interval [0, 2]. Compute the trapezoid and midpoint approximations t2 and m2. Solution: the length of each subinterval of [0, 2] is: [f (0) + 2f (1) + f (2)] 2! (2 0 02) + 2(2 1 12) + (2 2 22)" Problem 3 solution: the region enclosed by the graphs of the functions y = x and y = x from x = 0 to x = 1 is rotated about the y-axis. Solution: we will use the shell method to compute the volume.
